Prime p₀= 1458644069197759121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 118 2 10 2 76 2 88 2 22 2 (?)
a_n: 0 2 66 68 186 188 198 200 276 278 366 368 390 392
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 392
Found by: [SG-2W]Kurzer
db: batch=78, k=14, 64 118 10 76 88 22

STPT(10)	1458642655536856001	0 2 36 38 78 80 120 122 156 158	-1413660903120
STPT(10)	1458642720828403289	0 2 12 14 90 92 168 170 180 182	-1348369355832
TPT(14)	1458642826938204959	0 2 18 20 72 74 162 164 210 212 240 242 282 284	-1242259554162
SPT(16)	1458642862982154767	0 32 54 84 92 140 170 192 212 234 264 312 320 350 372 404	-1206215604354
SPT(16)	1458643332904175881	0 60 112 126 130 196 210 228 250 268 282 348 352 366 418 478	-736293583240
STPT(10)	1458643399858633169	0 2 18 20 30 32 42 44 60 62	-669339125952
STPT(10)	1458644339265374081	0 2 6 8 18 20 30 32 36 38	270067614960
SPT(18)	1458644492160291727	0 30 40 82 106 144 174 222 244 252 274 322 352 390 414 456 466 496	422962532606
SPT(16)	1458644841186883271	0 48 78 96 98 116 126 132 236 242 252 270 272 290 320 368	771989124150
STPT(10)	1458645128654893757	0 2 30 32 42 44 54 56 84 86	1059457134636
STPT(10)	1458645177230052809	0 2 48 50 90 92 132 134 180 182	1108032293688